edu.jas.gb

Class SolvableGroebnerBaseSeq<C extends RingElem<C>>

java.lang.Object

edu.jas.gb.SolvableGroebnerBaseAbstract<C>

edu.jas.gb.SolvableGroebnerBaseSeq<C>

Type Parameters:

C - coefficient type

All Implemented Interfaces:

SolvableGroebnerBase<C>

public class SolvableGroebnerBaseSeq<C extends RingElem<C>>
extends SolvableGroebnerBaseAbstract<C>

Solvable Groebner bases sequential algorithms. Implements common left, right and twosided Groebner bases and left, right and twosided GB tests.

Author:

Heinz Kredel.

Field Summary

Fields inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract

blas, red, sred, strategy

Constructor Summary

Constructors

Constructor and Description
SolvableGroebnerBaseSeq() Constructor.
SolvableGroebnerBaseSeq(SolvableReduction<C> sred, PairList<C> pl) Constructor.

Method Summary

Methods

Modifier and Type	Method and Description
SolvableExtendedGB<C>	extLeftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Solvable Extended Groebner base using critical pair class.
boolean	isLeftReductionMatrix(SolvableExtendedGB<C> exgb) Test if M is a left reduction matrix.
java.util.List<GenSolvablePolynomial<C>>	leftGB(int modv, java.util.List<GenSolvablePolynomial<C>> F) Left Groebner base using pairlist class.
SolvableExtendedGB<C>	minimalSolvableExtendedGB(int flen, java.util.List<GenSolvablePolynomial<C>> Gp, java.util.List<java.util.List<GenSolvablePolynomial<C>>> M) Minimal solvable extended groebner basis.
java.util.List<java.util.List<GenSolvablePolynomial<C>>>	normalizeMatrix(int flen, java.util.List<java.util.List<GenSolvablePolynomial<C>>> M) Normalize M.
java.util.List<GenSolvablePolynomial<C>>	twosidedGB(int modv, java.util.List<GenSolvablePolynomial<C>> Fp) Twosided Groebner base using pairlist class.

Methods inherited from class edu.jas.gb.SolvableGroebnerBaseAbstract

extLeftGB, isLeftGB, isLeftGB, isLeftReductionMatrix, isRightGB, isRightGB, isTwosidedGB, isTwosidedGB, leftGB, leftMinimalGB, rightGB, rightGB, twosidedGB

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SolvableGroebnerBaseSeq

public SolvableGroebnerBaseSeq()

Constructor.

SolvableGroebnerBaseSeq

public SolvableGroebnerBaseSeq(SolvableReduction<C> sred,
                       PairList<C> pl)

Constructor.

Parameters:

sred - Solvable reduction engine

pl - pair selection strategy

Method Detail

leftGB

public java.util.List<GenSolvablePolynomial<C>> leftGB(int modv,
                                              java.util.List<GenSolvablePolynomial<C>> F)

Left Groebner base using pairlist class.

Parameters:

modv - number of module variables.

F - solvable polynomial list.

Returns:

leftGB(F) a left Groebner base of F.

extLeftGB

public SolvableExtendedGB<C> extLeftGB(int modv,
                              java.util.List<GenSolvablePolynomial<C>> F)

Solvable Extended Groebner base using critical pair class.

Parameters:

modv - module variable number.

F - solvable polynomial list.

Returns:

a container for an extended left Groebner base of F.

twosidedGB

public java.util.List<GenSolvablePolynomial<C>> twosidedGB(int modv,
                                                  java.util.List<GenSolvablePolynomial<C>> Fp)

Twosided Groebner base using pairlist class.

Parameters:

modv - number of module variables.

Fp - solvable polynomial list.

Returns:

tsGB(Fp) a twosided Groebner base of Fp.

normalizeMatrix

public java.util.List<java.util.List<GenSolvablePolynomial<C>>> normalizeMatrix(int flen,
                                                                       java.util.List<java.util.List<GenSolvablePolynomial<C>>> M)

Normalize M. Make all rows the same size and make certain column elements zero.

Parameters:

M - a reduction matrix.

Returns:

normalized M.

isLeftReductionMatrix

public boolean isLeftReductionMatrix(SolvableExtendedGB<C> exgb)

Test if M is a left reduction matrix.

Specified by:

isLeftReductionMatrix in interface SolvableGroebnerBase<C extends RingElem<C>>

Overrides:

isLeftReductionMatrix in class SolvableGroebnerBaseAbstract<C extends RingElem<C>>

Parameters:

exgb - an SolvableExtendedGB container.

Returns:

true, if exgb contains a left reduction matrix, else false.

minimalSolvableExtendedGB

public SolvableExtendedGB<C> minimalSolvableExtendedGB(int flen,
                                              java.util.List<GenSolvablePolynomial<C>> Gp,
                                              java.util.List<java.util.List<GenSolvablePolynomial<C>>> M)

Minimal solvable extended groebner basis.

Parameters:

Gp - a left Groebner base.

M - a left reduction matrix, is modified.

Returns:

a (partially) reduced left Groebner base of Gp in a container.